Question

For each of the following solutions, the mass of solute is given, followed by the total volume of the solution prepared. Calculate the molarity of each solution. a. \(5.59 \mathrm{~g} \mathrm{CaCl}_{2} ; 125 \mathrm{~mL}\) b. 2.34 g \(\mathrm{CaCl}_{2} ; 125 \mathrm{~mL}\) c. 8.73 g \(\mathrm{CaCl}_{2} ; 125 \mathrm{~mL}\) d. 11.5 g \(\mathrm{CaCl}_{2} ; 125 \mathrm{~mL}\)

Short answer

The molarities of the solutions are: a) 0.403 M, b) 0.169 M, c) 0.629 M, and d) 0.829 M.

Step-by-step solution

Calculate the Molar Mass of CaCl2

Calculate the molar mass of \(\mathrm{CaCl}_{2}\) using the atomic masses of Calcium (Ca) and Chlorine (Cl). The atomic mass of Calcium is 40.08 g/mol and the atomic mass of Chlorine is 35.45 g/mol. Molar mass of \(\mathrm{CaCl}_{2} = \mathrm{1} \times \mathrm{40.08}~\mathrm{g/mol~(for~Ca)} + \mathrm{2} \times \mathrm{35.45}~\mathrm{g/mol~(for~Cl)} = 110.98\mathrm{~g/mol}\)

Calculate the Number of Moles of Solute

Calculate the number of moles (n) of \(\mathrm{CaCl}_{2}\) in each solution using the formula: \(\mathrm{n}=\frac{\mathrm{mass~of~solute}}{\mathrm{molar~mass~of~solute}}\) a. \(\mathrm{n}=\frac{5.59~g}{110.98~g/mol}=0.0504~mol\) b. \(\mathrm{n}=\frac{2.34~g}{110.98~g/mol}=0.0211~mol\) c. \(\mathrm{n}=\frac{8.73~g}{110.98~g/mol}=0.0786~mol\) d. \(\mathrm{n}=\frac{11.5~g}{110.98~g/mol}=0.1036~mol\)

Calculate the Volume in Liters

Convert the volume of each solution from milliliters to liters by dividing by 1000. a. \(125~\mathrm{mL} = 0.125~\mathrm{L}\) b. \(125~\mathrm{mL} = 0.125~\mathrm{L}\) c. \(125~\mathrm{mL} = 0.125~\mathrm{L}\) d. \(125~\mathrm{mL} = 0.125~\mathrm{L}\)

Calculate the Molarity of Each Solution

Calculate the molarity (M) of each solution using the formula: \(\mathrm{M}=\frac{\mathrm{moles~of~solute}}{\mathrm{volume~of~solution~in~liters}}\) a. \(M=\frac{0.0504~\mathrm{mol}}{0.125~\mathrm{L}}=0.403~\mathrm{M}\) b. \(M=\frac{0.0211~\mathrm{mol}}{0.125~\mathrm{L}}=0.169~\mathrm{M}\) c. \(M=\frac{0.0786~\mathrm{mol}}{0.125~\mathrm{L}}=0.629~\mathrm{M}\) d. \(M=\frac{0.1036~\mathrm{mol}}{0.125~\mathrm{L}}=0.829~\mathrm{M}\)

Key concepts

Molar Mass

Molar mass is a crucial concept in chemistry, as it provides the bridge between grams and moles—the unit of measurement in the molecular scale. To understand molar mass, think of it as the weight of all the atoms in a molecule. For example, to calculate the molar mass of calcium chloride (CaCl 2 ), we need to know the atomic masses of calcium (Ca) and chlorine (Cl).

• Calcium has an atomic mass of 40.08 grams per mole.
• Chlorine has an atomic mass of 35.45 grams per mole.

Since each calcium chloride molecule consists of one calcium atom and two chlorine atoms, we calculate its molar mass as follows: - Molar mass of CaCl 2 = (1 x 40.08 g/mol) + (2 x 35.45 g/mol) = 110.98 g/mol. Knowing the molar mass helps us convert between the mass of a substance and the number of moles, which is a critical step in many calculations in chemistry.

Mole Concept

The mole concept is a foundational idea in chemistry that relates the mass of a substance to the number of particles it contains. It allows chemists to count atoms, molecules, and ions in a given mass of substance with precision and ease.A "mole" represents Avogadro's number, which is approximately 6.022 x 10²³ particles. This means one mole of any element or compound contains this number of atoms or molecules. For calculations like the ones in the exercise, we often use the formula to find the number of moles (n):\[ n = \frac{\text{mass of solute}}{\text{molar mass of solute}} \]For example, if you have 5.59 g of calcium chloride (CaCl2), you can find the number of moles by dividing the mass of the solute by its molar mass (110.98 g/mol):\[ n = \frac{5.59}{110.98} = 0.0504 \, \text{mol} \]This mole value is then used to determine the concentration or react in further chemical equations.

Solution Concentration

Solution concentration is about describing how much solute is present in a given volume of solution. Molarity (M) is the term used to express concentration in chemistry, and it tells you the number of moles of solute per liter of solution.To calculate molarity, use the equation:\[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]For instance, given you have 0.0504 moles of CaCl2 in a 125 mL solution, first convert the volume to liters (125 mL = 0.125 L). Then calculate the molarity:\[ M = \frac{0.0504}{0.125} = 0.403 \, \text{mol/L} \]It's important to convert the volume to liters since molarity is defined as moles per liter. Understanding molarity helps in preparing solutions accurately for experiments and in understanding the relationships and reactions between different chemical species in the solution.